In spirit, our proof follows the proof in [1]}, which follows [2]}. The difference between our proof and that in [1]} is that we derive \(p(\mathbf {x}|\mathcal {C})\)  from \(p(\mathbf {z}|\mathcal {C})\)  while they derived \(p(\mathbf {z}|\mathcal {C})\)  from \(p(\mathbf {x}|\mathcal {C})\) .
